Both Piggy and Ralph share the bond of trying to use reason and logic. Both boys see the importance of what they have learned from adults, such as parents and teachers, and try to apply it to the island situation.
In chapter 1, a governing body is more or less set up. It is agreed that a leader needs to be elected in order to make decisions for the group. Ralph is elected and begins dividing up the workload among all of the boys. It's exactly what he would have seen at home with any business, school, or household.
Piggy as well is a source of great knowledge from "before the island." It's why he is so valuable at first. The boys cannot light a fire until Piggy imparts his knowledge of science to the boys. He creates fire by focusing solar light with his glasses.
Both boys, in their own way, represent an attachment to the old, pre-island way of life. That's their bond, and that is why Jack isn't fond of either of them.